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arXiv · 2601.03987

An SU(2n)-valued nonlinear Fourier transform

Michel Alexis·Lars Becker·Diogo Oliveira e Silva·Christoph Thiele
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Abstract

We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable sequences on the half-line, and construct an inverse for $SU(2n)$-valued functions whose diagonal $n \times n$ blocks are outer matrix functions. As an application, we relate this nonlinear Fourier transform with quantum signal processing over $U(2n)$ and multivariate quantum signal processing.

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Michel Alexis, Lars Becker, Diogo Oliveira e Silva, Christoph Thiele. 2026-01-07. An SU(2n)-valued nonlinear Fourier transform. https://arxiv.org/abs/2601.03987

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